Steve Jobs took to a stage a dozen years ago this week to introduce a revolutionary new product to the world: the first Apple iPhone.

That groundbreaking device, and the competitors that followed, changed the way people communicated, ordered dinner and hailed a taxi. The technology world reoriented around the smartphone, supplanting the personal computer, MP3 players, the digital camera and maps. And the mobile economy was born.

Today, it looks like the era of smartphone supremacy is starting to wane. The devices aren’t going away any time soon, but their grip on the consumer is weakening. A global sales slump and a lack of hit new advancements has underlined a painful reality for the matured industry: smartphones don’t look so singularly smart anymore.

While once smartphones were like a centripetal force sucking up tools from dozens of devices, from flashlights to calculators to game consoles, functions are now flying out of phones and onto other products with their own embedded smart connections. Wristwatches can now text emojis. Televisions can talk and listen. Voice-activated speakers can order diapers.

The number of “connected” devices in use that can stream music, clock mileage or download apps has more than doubled to 14.2 billion in the past three years, according to market researcher Gartner Inc. The total excludes smartphones.

What’s shifted most is the smartphone’s monolithic status as the device that software companies and businesses needed to reach mobile users-and for consumers to access their services. Now the universe has expanded to voice apps, car infotainment centers and wearable devices.

“We may even need another word for whatever the smartphone will become because when ‘smart’ is everywhere that term becomes almost meaningless,” said Wayne Lam, a principal analyst at research firm IHS Markit .

Like the arc of the personal computer, smartphones-now more a need in the modern world than a luxurious splurge-are engaged in a race toward the bottom. The industry’s two titans, Apple Inc. and Samsung Electronics Co. , risk seeing their high-end phones become commoditized, as Chinese rivals Huawei Technologies Co. and Xiaomi Corp. prove capable of making similar devices at lower prices.

Twelve years after the iPhone’s debut, more than half of the world’s population owns a smartphone. While that leaves billions of potential first-time buyers in countries from Indonesia to Brazil, they reside in poorer areas, offering lower profits. Meanwhile, the market in wealthier countries such as the US has become saturated, as the improvements in the devices become more incremental and many consumers have decided they don’t need to get each new upgrade.

As recently as 2015, annual smartphone shipments grew at a double-digit clip. Those days are over: The industry saw its first declines at the end of 2017 and remained negative all last year. A major driver was China, the world’s largest smartphone market, where annual shipments sank 16%, according to government data.

Apple earlier this month made a rare cut to its quarterly revenue forecast, citing slower-than-expected iPhone sales in China. Samsung followed with a warning of its own, telling investors its fourth-quarter operating profit would decline 29%. The South Korean company feels the smartphone strain doubly, as a handset maker and a components supplier to many rivals, including Apple.

Cao Yuqian, a 24-year-old student in Shanghai, had long made a habit of buying a new phone every year-her iPhone 8 Plus is her 10th Apple device.

But this year, she’s in no rush to upgrade because leaping to the next generation of iPhones would mean losing the physical home button on the front of the device. And there’s another reason. “Now it’s a bit pricey,” Ms. Cao said. Apple Chief Tim Cook this past week stressed that the company’s product pipeline is strong and touted the success it has had beyond the iPhone, selling wearables such as its AirPod wireless headphones and the Apple Watch.

The picture is different in India, where fewer than one in four people own a smartphone and its user base is growing faster than any other country. But the average price for a smartphone there is about $160, or half of what most of the world typically spends, IDC says.

In developed markets, smartphone usage may be reaching its upper limits, as some consumers pull back amid the tech industry’s acknowledgment their products can be addictive, spur anxiety, distract drivers and cast a pall of silence over the dinner table.

Apple and Facebook Inc., for instance, have created systems that track users’ screen time and notify them when they’ve reached preset limits.

Brian McElhaney, 32, an actor, writer and director in New York, became so concerned with his smartphone usage that last year he ditched his iPhone for a $35 flip phone. He only reaches for his deactivated smartphone at night-on his home Wi-Fi-when he needs to access social media apps to post work content and says he can go days without touching it.

“I went whole hog into this technology without really knowing what it was going to do to me,” Mr. McElhaney said of smartphones.

More than a third of consumers look at their smartphones within five minutes of waking up and about 20% said they check their phone more than 50 times a day, a Deloitte survey of 53,000 people in countries around the world found.

Americans on average spend two hours and 33 minutes daily looking at their smartphones in 2019, some 7% more than the prior year, according to eMarketer, which said the rate of growth has slowed from previous years. When Mr. Jobs, then Apple’s chief executive, introduced the iPhone from a stage at the Macworld expo in San Francisco in 2007, the crowd burst out clapping the first time he showed them how the phone could be unlocked by swiping a finger across the screen. When he used his finger to scroll through the music on the phone, they cheered.

For years afterward, phone makers would routinely amaze consumers with new advancements, from selfie cameras to waterproof designs to plus-size screens. The early flourishes, though, have more than satiated a wide swath of consumers who aren’t lured by wireless charging or augmented reality.

As advances became more incremental, Apple and Samsung saw their once-sizable gaps narrow with lower-cost Chinese rivals like Huawei, Xiaomi and BBK Electronics Corp.’s Oppo. Chinese vendors now make the majority of the world’s phones-crossing that threshold for the first time last year, according to Canalys, a market researcher.

The handset industry is hopeful the forthcoming next-generation 5G networks, which could be 100 times faster in speed, will unlock new uses for the smartphone and entice people to upgrade en masse. Some of those planned changes include better syncing with cars, kitchen appliances and home electronics.

“I don’t think we’ve hit peak utility for the smartphone. I think it continues to grow in importance in our lives,” said John Foster, CEO of Aiqudo, a platform that creates voice-enabled commands for mobile apps. While the earliest 5G-compatible smartphones are expected to be released to U.S. consumers early this year, carriers are still in the process of upgrading their networks. There will likely be pockets of service in the U.S. in 2019, but widespread network buildout and adoption by consumers and businesses is likely to take years.

Smart-home devices from speakers to home assistants to connected refrigerators offer the ability to relay the weather or guide consumers through recipes, tasks that until recently had fallen to smartphones.

Michael Woods, a 32-year-old federal government attorney in Washington, D.C., said his New Year’s resolution is to reduce his screen time, something his two Amazon Echos and Google Home hub help him with. “Not because I want to get rid of my phone, but just because I want to be more present,” he said.

The breadth of connected gadgets has made it harder to unplug. But the more nascent additions tug on people’s attention differently than smartphones, a potential allure for people irritated by the flurry of notifications from their phones, said Kai Lukoff, a University of Washington researcher studying problematic smartphone use. “With a smart speaker, it only responds to requests I make of it,” Mr. Lukoff said.

A growing number of children have smartphones and new younger users contributed to Verizon Communications Inc.’s larger-than-expected subscriber growth in the fourth quarter, the carrier said last week. But those devices are no longer the only avenue to private social interaction for children and tweens, many of whom now enjoy their own tablets and gaming systems complete with headsets that allow them to talk regularly with friends without a phone.

Device makers will have to prove that they can emerge from what some consumers see as years of marginal improvements in camera, battery and security functionality.

Rick Berkowitz, a 65-year-old in St. Louis, uses his new iPhone XR to monitor stocks, cast yoga videos onto his TV and FaceTime his grandchildren. But the features, other than unlocking his device with facial recognition, leave him unimpressed. “I personally believe that all these phones have pretty much reached their zenith just like the PCs did,” said Mr. Berkowitz, who runs his own hedge fund. The challenge tech companies, wireless carriers and device makers now face is birthing the next society-shifting technology. “What’s not going to go away: the need to have a device that’s constantly with you, to remote control your life. At the moment, we call that the smartphone,” said Jaede Tan, a regional director at App Annie, which tracks smartphone behavior. “Does it become smaller, sit on your wrist, a chip in the back of your mouth? Maybe. The concept needs to remain constant.”